1. Field of the Invention
The present invention relates to exponential generator circuits, and particularly to a high dynamic range exponential current generator utilizing MOSFETS operating in the weak inversion mode.
2. Description of the Related Art
An exponential function generator produces an output waveform (current/voltage) which is an exponential function of the input waveform (current/voltage). The exponential characteristics can be easily obtained in BiCMOS or Bipolar technologies using the intrinsic characteristics (IC/VBE) of the bipolar transistors. Though, it is not easy to realize such function in CMOS technology because of the inherent square-law or linear characteristics of MOSFETs operating in the strong inversion region. So the widely used technique to implement analog exponential function circuits using MOSFETs in strong inversion is based on pseudo-approximations. To mathematically implement the exponential function by this method, different approximations have been already introduced; Taylor series 2nd order, Taylor series 4th order, Pseudo exponential, Pseudo-Taylor approximation, Modified Pseudo-Taylor approximation, additional approximations have been proposed.
A MOSFET device biased in weak inversion region is a well-known approach to introduce an exponential function due to the exponential relationship between IDS and VGS of MOSFET in weak inversion regime. Referring to IDS/Vgs relationship, the drain current of MOSFET in weak inversion region is given by:
      I    DS    =      2    ⁢    n    ⁢                  ⁢          μ      n        ⁢          C      ox        ⁢          W      L        ⁢          V      T      2        ⁢          ⅇ              (                                            V              gs                        -                          V              th                                            nU            T                          )            
Although the low VGS voltage makes this technique efficient in low voltage applications compared with approximations that use MOSFET in strong inversion regime but, obviously, the exponential relation between IDS and VGS is not perfect because it suffers from strong temperature dependency, threshold voltage variation effect and sensitivity against process variation. Therefore, it is highly preferred to design an exponential function generator that provides accurate and stable exponential function vs. temperature variation; provides a robust and efficient design versus the supply voltage variation; utilizes current-input current-output exponential generator thereby providing higher frequencies of operation and wider dynamic ranges and extended output range with minimum linearity error.
Thus, a high dynamic range exponential current generator with MOSFETs solving the aforementioned problems is desired.